I'm having a problem with my air conditioning. Actually it's the blower for both my air conditioning and my furnace.

I'd say about 75% of the time the blower does not turn on (whether in auto or if you manually turn it to "always on") mode. However, the air conditioning always turns on (just the blower doesn't start).

Sometimes if I go out and remote the furnace panel and put it back on it will start. Sometimes it will start and immediately shut off. Sometimes it will continuously cycle on and off (even if the fan is in the always on position). Most of the time I can hear clicking associating right before the fan turns on and off (like a relay/switch being thrown). Sometimes the sound is like machine gun fire because it is constantly turning on and off that quickly.

I've tried a few different troubleshooting steps, but I'm at a complete loss. Any thoughts?

You might check the blower door switch for proper operation. It is a safety device designed to prevent the unit from operating if the blower door is removed. This switch has caused this type of problem in the past. Also a loose low voltage control wire or a defective blower relay can also cause this trype of a problem. When you remove and reinstall the furnace panel you are moving things around and that leeds me to the fact that something like wiring is loose or a control not properly seated.